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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>As another example, Suppose a 25 year-old plans to set aside a fixed amount every year of his/her working life, invests at a real return of <span class="process-math">\(6\%\text{,}\)</span> and retires at age 65. How much must he/she invest each year to have <span class="process-math">\(8,000,000\)</span> at retirement? Let <span class="process-math">\(S(t)\)</span> be the value of the investment at time <span class="process-math">\(t\text{,}\)</span> and let <span class="process-math">\(r\)</span> be the annual interest rate compounded after every time interval <span class="process-math">\(\Delta t\text{.}\)</span> We can also include deposits and let <span class="process-math">\(k\)</span> be the annual deposit amount, and suppose that an installment is deposited after every time interval <span class="process-math">\(\Delta t\text{.}\)</span> The value of the investment at the time <span class="process-math">\(t+ \Delta t\)</span> is then given by</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\label{eq1_7}
S(t+ \Delta t) = S(t)+(r \Delta t)S(t) +k \Delta t
\end{equation*}
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<p class="continuation">where at the end of the time interval <span class="process-math">\(\Delta t\text{,}\)</span> <span class="process-math">\(r \Delta t S(t)\)</span> is the amount of interest credited and <span class="process-math">\(k \Delta t\)</span> is the amount of money deposited <span class="process-math">\((k&gt;0)\text{.}\)</span></p>
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